Fragment Size Distribution As A Smoking Gun Of Asteroid Family Formation

Among the asteroids, small worlds orbiting the Sun between Mars and Jupiter, we find those genetically related to each other. They are members of the so-called asteroid families. These asteroids have very similar orbits and other physical characteristics, such as spectra.

Exactly 100 years ago, these were noticed by a Japanese astronomer Kiyotsugu Hirayama, and the current view of the asteroid families is that they are groups of asteroids originating from a single large asteroid. This parent asteroid was hit by another asteroid in the past and was either completely disrupted into pieces of various sizes or it was heavily cratered and the ejected material formed the asteroid family.

Asteroid families provide us with a unique source of information about asteroids. They are huge natural laboratories because they bear information about the giant collision that formed the family as well as about the internal structure and composition of the parent asteroid.

One of the pieces of information are the sizes of individual members of the family or, in other words, the pieces of the parent asteroid that was originally disrupted to form the family. When we order the members by their size, we can plot what we call size-frequency distribution (or SFD) of the family, and from its characteristics, we can deduce more about the collision. In Fig. 1 we see SFD’s of some asteroid families including one very intriguing family we focused on in our paper, the Datura family.

Figure 1: The fragment distributions of various asteroid families. The Datura family is plotted with red open squares. The legend contains some basic information about the families, its name, the estimated mass ratio of the largest and parent asteroid, collision severity, age in millions of years and the diameter of the largest family member. Republished with permission from Elsevier from: https://doi.org/10.1016/j.icarus.2017.05.018

The Datura family was discovered and recognized as a very young family by Nesvorný et al. (2006). It’s located in the Main asteroid belt and as was later found that family was formed quite recently, merely 0.5 million years ago, by a cratering event on a small asteroid 1270 Datura, only 8 km in diameter. The Datura family is not a large family when it comes to the sizes of its members or when it comes to their number. Today we only know 17 confirmed members of this family. That is mainly caused by a large observational bias.

What is the observational bias? It is an effect which arises from our limited ability to see tiny and dim asteroids with our telescopes. Our observation is more sensitive to large and not so distant ones because these asteroids reflect much more light we can detect. Then we say our observation is biased towards brighter asteroids. Nevertheless, due to a measured bias of our telescopes, it was possible to estimate what the real SFD of the family might look like (Vokrouhlický et al., 2017).

Now comes the interpretation phase. When we look at the SFD of the Datura family, it looks distinctly different from the SFD’s of other families. The possible debiased SFD of the Datura family (dot-dashed line in Fig. 1), however, is not so different. It is only shifted towards smaller sizes because the Datura members are small asteroids. It also bends as the SFD’s of other families to a shallower slope. Notice that it roughly bends at the similar size of 1–2 km for all plotted families. Why is that so? We think that this is mainly caused by the observational bias. Main belt asteroids about a few km in diameter are roughly the smallest that we can routinely discover and observe. We also observe smaller ones, but it’s rather rare. So the SFDs probably bend because we observe too little asteroids of this size or smaller that could be recognized as family members.

Small asteroids, when properly shaped, can be gradually spun up or down by the re-emission of the sunlight from their surface layers and eventually can start to shed material and even be torn apart. This process is called the Yarkovsky–O’Keefe–Radzievskii–Paddack (or YORP) effect. Based on this, Vokrouhlický et al. (2017) proposed another mechanism that could be responsible for a different SFD of the Datura family. Namely, it could possibly be explained by a collision of the nearly critically-rotating 1270 Datura with a comparably smaller projectile. It means that before the family was formed, 1270 Datura was spinning so fast that some of the parts on its equator were almost spinning off of its surface. This hypothesis needs to be checked presumably by numerical simulations.

The lower slope of the SFD could also be explained by missing family members that could have been destroyed either by the above mentioned YORP effect or by collisional grinding. We calculated the probabilities of such processes given the young age of the Datura family and we got very low numbers on the order of a few percents for the smallest members and only a few tenths of a percent for the largest family members. In other words, the small asteroids that belong to Datura are still there, but we don’t see them yet.

There is one notable feature we can see in the SFD’s of some asteroid families. It looks like a bump, and it usually occurs between second and fifth family member. We noticed this feature also in Datura’s SFD and although it could also be explained by an observational bias, we started to think about other possibilities. Moreover, we also know that some of the largest fragments are very elongated asteroids or maybe contact binary asteroids (two asteroids sitting upon each other). This is quite typical for the so-called spall craters that we observe in every small-scale laboratory impact experiment. Could there be a large spall crater on Datura? The answer is yes!

We hypothesize that the Datura family could have been formed by spall cratering on the surface of 1270 Datura based on the scaling of impacts into a rocky material Datura is probably made of and taking Datura’s small size into account. This would explain the bump in the SFD and also the elongated shape of the largest family members. We also compared the observed SFD of the Datura family to the size distributions of small-scale laboratory impact experiments that are known to produce spall craters, and there is a close match.

To conclude, the SFD of the very young Datura family differs from other family size distributions due to observational bias. Most of its known members are smaller than those in other families and that explains the low number of the known family members and also the apparent shallowness of the SFD. The bump in the SFD can be explained by the spall cratering that we commonly observe in small-scale laboratory impact experiments.

About The Author

TH

Tomáš Henych

Tomáš Henych is a researcher affiliated with the University of Washington. He is mostly interested in asteroid families and their collisional origin and interpretations of their SFD's. In our last project we focused on collisional evolution of asteroid spins and shapes and their collisional lifetimes. He received his Ph.D. from Masaryk University in 2013.

Keith Holsapple

Keith Holsapple has been a professor in Aeronautics & Astronautics since 1965. With a background in structures, engineering mechanics and numerical methods, his research interests are now focused on hypervelocity impacts and material and numerical modeling. He has been active in the studies of mitigation methods for Earth-threatening asteroids, has presented talks at various AIAA and NASA sponsored meetings and has performed code calculations of the mitigation of threatening asteroid and comets by impacts and by nuclear weapons.

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